GeRgraphy

16 March, 2016

GIS

Geographic Information Systems

GIS

Geographic Information Systems

incorporating
storing
manipulating
analyzing
displaying…

Spatial Data

What is spatial data?

Nonspatial data has no location information

nonspatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4)
)
print(nonspatial)

##   id       data
## 1  1  1.1327954
## 2  2 -0.3140816
## 3  3 -0.2447371
## 4  4  0.7490857

What is spatial data?

Spatial data has location information

The simplest spatial data are points on a map

spatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4),
  x=runif(4,-180,180),
  y=runif(4,-90,90)
)
print(spatial)

##   id       data          x          y
## 1  1 -0.3386280 -110.90702  16.393213
## 2  2  0.7831824  178.54540  -4.378136
## 3  3  0.4201943  153.38047 -39.811305
## 4  4  0.9755812  -94.22992 -43.465543

What is spatial data?

Which we can convert to explicitly spatial data using the sp package. Most GIS packages in R store data as sp classes.

library(sp)

What is spatial data?

The sp package has a method called coordinates that converts points to an sp class.

coordinates(spatial) = ~ x + y
class(spatial)

## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"

plot(spatial, axes=T)

What is spatial data?

Spatial data also needs a reference system or "projection" that allows us to represent spatial features on a map. Projections can be thought of as simply a coordinate system with an origin that is relative to a known point in space.

This is a whole field of mathematically intensive study termed "geodesy"

Much of the field of geodesy is jam-packed in the rgdal package, which is a wrapper for the Geospatial Data Abstration Library

library(rgdal)

What is spatial data?

rgdal includes a comprehensive list of projections that are typically represented as a string of parameters.

The most common is our standard latitude/longitude system, where the coordinates are angular and the origin is the equator directly south of Greenwich, England. The simplest projection string to denote this projections is:

"+proj=longlat"

To define the projection for spatial, we write to its proj4string slot:

proj4string(spatial) = "+proj=longlat"

Projections are a necessary evil for GIS users (to be continued)

What is spatial data?

With a projection associated with our spatial data, we can now relate it to other spatial data. In other words, let's make a map!

library(leaflet)

m = leaflet(data=spatial) %>%
  addTiles() %>%
  addMarkers()
m

What is spatial data?

Arguably, the most common use of spatial data, and therefore GIS, are in data exploration, simply taking a look at where the phenomenon occur. This is useful in the sense that we can see obvious trends in the data, giving clues for further analysis, or merely checking our work, seeing if we have made mistakes. Additionally, spatial data is used for different kinds of analysis, leveraging the location data to make inferences. This analysis could take the form of selecting all wells that fall within certain soil types or in the construction of error terms in construction a statistical model.

Maybe delete this paragraph… The most common software used in GIS are ArcGIS, produced by ESRI and QGIS, an open source analog, but there are many other software packages for GIS, both propietary and open-source. Any familiarity with the most popular GISs will show you that they are GUI-based and therefore much different from the look and feel of R, and, while R is not necessarily a replacement for the ArcGIS or QGIS, the analysis and plotting capability of R makes it a powerful GIS, and when it comes to model construction, R, and no suprise here, blows the common GIS platforms out of the water.

Spatial data types

Two main types: vector and raster

Vector = Polygons
Raster = Grid

Vector = Discrete
Raster = Continuous

Vector = Illustrator/Inkscape
Raster = Photoshop/GIMP

Maybe break this apart and put this into the respective intros of the datatypes below? Spatial data are divided up into two kinds of data, vector data and raster data. Vector data consist of the location data being defined by points. There are three main kinds of vector data: points, lines and polygons. Point data, as might be guessed, are data where each observation is defined by one coordinate pair, X and Y. In line data each observation is defined by a series of coordinate pairs that define a one dimensional path in space. Polygons are data where each observation is defined by coordinate pairs that trace out a two-dimensional area. Common uses of vector data are for phenomenon that have discrete boundaries and locations, e.g., wells and bird sitings for points, rivers and streets (at certain scales) for lines, and county borders and soil types for polygon data. Raster data are constructed as grids that are laid out over an area. Each cell of the grid contains some information about the phenomenon, but each cell will not be explicitly given a coordinate pair, rather every cell has the same length and width and so only the certain corners of the data need to be given coordinate pairs. Precipitation and temperature data are often portrayed as raster data because of the way they vary continuously over the space. Examples of the creation, input, and output of these data types are given below.

Note to power users: The usual definitions of these data describe vector data as being for data with discrete boundaries and raster data for that which continuously varies. While this is true in general, it is essentially a matter of convenience that determines which type is best. For example, you could represent a dataset of bird sitings in a raster format, but because the grid is so sparse (NA or 'no siting' for nearly all the cells) it saves memory (and makes more inuitive sense) to store the data as points. Conversely, rainfall data can be stored as thousands of points, each marking the estimated rainfall at that location, but storing the data in this format is rather cumbersome if the area is large.

This presentation is meant to give an introduction to handling spatial data in R. It's intended audience are those with at least a basic knowledge of R and an interest in, though not necessarily knowledge of, working with spatial data. We will cover basic handling and manipulation of vector data and raster data, and then give a flyover of how coordinate reference systems work and how to work with them in R.

Vector Data

Vector Data Intro

How data is represented Vector data is represented by coordinate pairs,

Figure depicting * Points

Lines
Polygons

Vector Data Intro

Geometry is associated with other data, attribute data Conceptualize as a row in a table

What vector data is used for
Geometry is just another field in the table, mention multipart features

Outline 2

Part I

introduce soils data, ways of looking at it
well data, read in and convert
plot the two, brief discuss issues with CRS matching
Example scenario, demo gIntersects and how to use introduce other types of spatial relations
Use over to extract attributes and select those above a threshold of sand
Introduce buffering and suggest trying with that

Vector Data Basics

Data Input/Output

library(rgdal)
soils = readOGR(
    dsn="data",
    layer="soilsData")

## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "soilsData"
## with 75 features
## It has 27 fields

writeOGR(
    soils,
    "data",
    "soilsData_out",
    driver="ESRI Shapefile"
)

Vector Data Basics

Other ways of creating of spatial data from list of coordinates:

wells = read.delim("./data/WellLocations.tsv")
class(wells); head(wells)

## [1] "data.frame"

##           x        y pts.data.id
## 1 -90.05145 43.10047           1
## 2 -90.05553 43.10470           2
## 3 -90.07305 43.09013           3
## 4 -90.04716 43.08454           4
## 5 -90.07198 43.08850           5
## 6 -90.06599 43.09197           6

coordinates(wells) <- ~ x + y
class(wells)

## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"

Vector Data Basics

Helper functions:

class(soils)

## [1] "SpatialPolygonsDataFrame"
## attr(,"package")
## [1] "sp"

slotNames(soils)

## [1] "data"        "polygons"    "plotOrder"   "bbox"        "proj4string"

length(soils)

## [1] 75

Vector Data Basics

str(soils@data[,1:10])

## 'data.frame':    75 obs. of  10 variables:
##  $ mukey  : Factor w/ 25 levels "2774742","2774772",..: 12 19 12 6 9 5 7 24 25 13 ...
##  $ muarcrs: Factor w/ 75 levels "0.40538405","0.90105194",..: 30 62 70 18 8 26 19 5 15 23 ...
##  $ Sand1  : num  21.5 11 21.5 12 29.5 ...
##  $ Sand2  : num  35.29 8.34 35.29 9.02 38.22 ...
##  $ Sand3  : num  45.09 7.56 45.09 16.59 64.52 ...
##  $ Sand4  : num  48.6 30.6 48.6 36.7 33.2 ...
##  $ Sand5  : num  0 31.1 0 27.1 57.2 ...
##  $ Silt1  : num  45.8 65.2 45.8 68.7 54.5 ...
##  $ Silt2  : num  37.3 64.9 37.3 60.3 43.5 ...
##  $ Silt3  : num  36.7 64.1 36.7 34 21.1 ...

Vector Data Basics

str(soils@polygons[1])

## List of 1
##  $ :Formal class 'Polygons' [package "sp"] with 5 slots
##   .. ..@ Polygons :List of 1
##   .. .. ..$ :Formal class 'Polygon' [package "sp"] with 5 slots
##   .. .. .. .. ..@ labpt  : num [1:2] 514199 291168
##   .. .. .. .. ..@ area   : num 10776
##   .. .. .. .. ..@ hole   : logi FALSE
##   .. .. .. .. ..@ ringDir: int 1
##   .. .. .. .. ..@ coords : num [1:21, 1:2] 514211 514206 514195 514178 514180 ...
##   .. ..@ plotOrder: int 1
##   .. ..@ labpt    : num [1:2] 514199 291168
##   .. ..@ ID       : chr "0"
##   .. ..@ area     : num 10776

Vector Data Basics

A number of common functions have methods for spatial data

silty = subset(soils, Silt1 > 70)
paste("There are", length(soils), "soil features total;")

## [1] "There are 75 soil features total;"

paste(length(silty), "with a silt percentage over 70")

## [1] "12 with a silt percentage over 70"

Vector Data Basics

Making simple maps is quite easy

par(mfrow=c(2,1), bg=NA)
plot(
    soils,
    main="Soils Polygons",
    col=rainbow(5))
plot(
    wells,
    main="Well Data",
    col='red'
)

Coordinate Reference Systems

A (Very) Brief Break

A coordinate reference system (CRS) defines the surface of the world. There are many and if they don't match, errors and issues can arise

Coordinate Reference Systems

A (Very) Brief Break

To illustrate issues:

soils = readOGR(
    dsn="data",
    layer="soilsData")
plot(
    soils,
    main="Soils",
    col=rainbow(5)
)
plot(
    wells,
    add=T
)

Hmmm, where are the points?

plot the two, brief discuss issues with CRS matching
Example scenario, demo gIntersects and how to use introduce other types of spatial relations
Use over to extract attributes and select those above a threshold of sand
Introduce buffering and suggest trying with that

Outline 3

Part II

introduce ward data
scenario for modeling: predict %dem turnout
use regular linear regression, moran I the residuals
construct neighborhood weights using adjacency and distance, then construct model
take a look at results

Outline 4

Part III

Scenario create map of %dem with indication of percent turnout.
Walk throug various iterations, raise problems then solve
plot just lines
introduce thematic mapping/choropleth mapping/data classification and coloring
Show classInt and creating the color vector
legend manipulation
creating centroids and scaling proportionally

Raster Data

Intro

A raster grid is rectangular.

Grid is another word for matrix.

Grid is another word for image.

A GIS raster grid is a matrix/image with an associated location and projection.

Intro

At a minimum, a GIS raster grid contains:

matrix of values
projection
reference point, often (x,y) of the lower-left corner
cellsize

Raster I/O

The rgdal rgdal packages is primarily for I/O and projecting GIS data

library(rgdal)

The raster package does everything rgdal does, but it includes lots of additional functionality.

library(raster)

Raster I/O

elev = readGDAL("data/dem_wi.tif")
writeGDAL(elev, "data/dem_wi_out.tif")

elev = raster("data/dem_wi.tif")
writeRaster(elev, "data/dem_wi_out.tif")

Raster data structure

The raster object elev has all the necessary pieces of spatial information:

elev

## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : /home/devans/Documents/GeRgraphyPresentation/data/dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster data structure

Which means we can make a map!

m = leaflet() %>%
  addTiles() %>%
  addRasterImage(elev, opacity=0.5)
m

Raster data structure

Raster analysis

Remember that rasters are just matrices!

Therefore, most matrix operations can be applied to rasters. For example:

plot(
  elev > 400,
  col=c("red", "blue")
)

Raster analysis

Rasters can be easily converted to matrices to do more complex work.

lat_grad = apply(
  as.matrix(elev),
  1,
  mean,
  na.rm=T
)
plot(lat_grad, type="l")

Raster overlay

Most raster analysis ultimately executes some sort of overlay.

The issue:

To overlay two or more rasters, their projections, extents, and cellsizes must align perfectly.

This can be a difficult task.

Raster overlay

coordinate systems

What is the highest point in each county?

# Pseudo-code
1. Read in elevation data (raster grid)
2. Read in county boundary data (polygons)
3. Convert counties to raster grid that aligns with elevation grid
4. Find maximum elevation gridcell within each county

Raster overlay

coordinate systems

counties = readOGR("data", "WI_Counties")

## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "WI_Counties"
## with 72 features
## It has 7 fields

elev

## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : /home/devans/Documents/GeRgraphyPresentation/data/dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster overlay

coordinate systems

proj4string(counties)

## [1] "+proj=tmerc +lat_0=0 +lon_0=-90 +k=0.9996 +x_0=520000 +y_0=-4480000 +ellps=GRS80 +units=m +no_defs"

proj4string(elev)

## [1] "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

Raster overlay

coordinate systems

extent(counties)

## class       : Extent 
## xmin        : 294839 
## xmax        : 770036.4 
## ymin        : 225108.8 
## ymax        : 734398.4

extent(elev)

## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

cty_grid = rasterize(counties, elev, field="COUNTY_FIP")
summary(cty_grid)

##          layer
## Min.        NA
## 1st Qu.     NA
## Median      NA
## 3rd Qu.     NA
## Max.        NA
## NA's    109908

Raster overlay

coordinate systems

prj = proj4string(elev)
cty_prj = spTransform(counties, prj)

To do this, we use the spTransform function in the sp package.

Raster overlay

coordinate systems

extent(cty_prj)

## class       : Extent 
## xmin        : -92.88924 
## xmax        : -86.8048 
## ymin        : 42.49197 
## ymax        : 47.08077

extent(elev)

## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

plot(elev)
plot(cty_prj, add=TRUE)

Raster overlay

coordinate systems

cty_grid = rasterize(counties, elev, field="COUNTY_FIP")
summary(cty_grid)

##          layer
## Min.        NA
## 1st Qu.     NA
## Median      NA
## 3rd Qu.     NA
## Max.        NA
## NA's    109908

Raster overlay

coordinate systems

extent(cty_grid)

## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

extent(elev)

## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

library(dplyr)
ovly = data.frame(
  elev=getValues(elev),
  cty=getValues(cty_grid)
)

hi_pt = ovly %>%
  group_by(cty) %>%
  mutate(
    elev = (elev == max(elev, na.rm=T)) * elev
  ) %>%
  ungroup()

elev = setValues(elev, hi_pt[["elev"]])
elev[elev == 0] = NA
hi_pt_sp = rasterToPoints(elev, spatial=T)